The present invention relates to a method for optimizing the image properties of at least two optical elements, in which at least one of the optical elements is moved relative to at least one stationary optical element.
The invention also relates to methods for optimizing the image properties of at least three optical elements, in which the relative position of the optical elements with respect to one another is adjusted.
Optical assemblies comprising at least one movable optical element are known on the market, and include projection objective lens systems for microlithography. With these, but also with other optical assemblies, a high image quality is required in order to produce a picture of a structure that is as free of defects as possible. The movability of at least one optical element within such a projection objective lens system serves to vary the image properties of the projection objective lens system with the aim of reducing the occurring image defects.
The choice of the position to which a moveable optical element should be adjusted so that the image defect of the optical assembly is thereby minimized, has hitherto often been made by individual measurement of the image properties of the optical elements before they are assembled. Since many image defects are produced only during assembly, for example as a result of pressure influences of the holders for the optical elements, such an approach to achieving a high image quality is too inaccurate.
Other approaches, in which the positioning of the optical elements is optimized on the basis of readily visualisable target quantities reproducing, though only incompletely, the image quality and that have been obtained from the interaction of the optical elements, rely on the experience of the technician entrusted with the adjustment of the assembly to find the most favorable rotational position. Such optimization methods are insufficiently deterministic.
A method that necessarily leads to the optimum relative position between the moveable and the stationary optical element takes measurements of the image defects of the optical assemblies, including both the moveable and the stationary optical elements, at all achievable positions of the movable optical element. This procedure is too tedious and complicated since as a rule a plurality of achievable positions exists for the accurate positioning of the movable optical element.
In the search for possible ways of improving projection objective lens systems in order to satisfy increasingly stringent requirements as regards image quality, projection objective lens systems have been proposed in which movable optical components can be arranged at various positions within the projection objective lens system. In this connection the number of movable optical components is not limited to one; instead there may often be several movable optical elements within the projection objective lens system.
With such projection objective lens systems the question arises, at which position should a movable optical element be provided within the projection objective lens system in order to be able to correct a specific image defect, and how many optical elements may optionally have to be moved for this purpose. In addition there is the question, what degree of freedom of movement can be employed in order to correct a specific image defect. Such degrees of freedom of movement include the rotation of optical elements within the projection objective lens system, the displacement of optical elements along the optical axis of the projection objective lens system (focusing) and vertical thereto (centering), and the tilting of optical elements within the projection objective lens system.
Overall there exists a plurality of degrees of freedom that are in principle available for correcting image defects within a projection objective lens system.
With the previously known optical assemblies a choice of the degrees of freedom that were employed for correcting image defects was made on the basis of trial-and-error methods. In the same way as when finding the most favorable rotational position, here too the experience of the respective technician was decisive in finding useful degrees of freedom, which however led to adjustment results that were not deterministically reproducible. Often the choice of the lenses to be moved as well as the choice of the degrees of freedom of movement were very time-consuming and also did not always achieve predefined specifications.
Also in those cases in which it is in principle known which lenses within a projection objective lens system have to be moved in order to correct specific image defects, as a rule a multidimensional problem still always exists with a mobility of several lenses within a projection objective lens system, with the result that an optimal position configuration of all movable lenses in which the overall image defect falls below predetermined specifications and/or reaches an absolute minimum often cannot be found with reasonable effort and expenditure.
A first object of the present invention is accordingly to provide a method for optimizing the image properties of at least two optical elements, in which at least one of the optical elements is moved relative to at least one stationary optical element, by means of which the overall image defect of the at least two optical elements can be specifically reduced with comparably little effort.
This object is achieved according to the invention by a method involving the following procedural steps:
a) measurement of the overall image defect of all optical elements, consisting of the image defect of the movable optical element and the image defect of the stationary optical element, in which all optical elements are traversed by measuring light;
b) representation of the measured overall image defect as a linear combination of the base functions of an orthogonal function set;
c) movement of the movable optical element relative to the stationary optical element to a new measurement position;
d) renewed measurement of the new overall image defect of all optical elements, consisting of the image defect of the movable element and the image defect of the stationary optical element, in which all optical elements are traversed by measuring light;
e) representation of the new overall image defect as a linear combination of the base functions of an orthogonal function set;
f) calculation of the image defect of the movable optical element and calculation of the image defect of the stationary optical element, using the representations obtained in steps b) and e);
g) calculation of a target position of the movable optical element from its image defect and from the image defect of the stationary optical element, in which the overall image defect is minimized;
h) movement of the movable optical element to the target position.
The method according to the invention first of all determines in situ the image defect contributions of the movable and of the stationary optical elements. This determination utilizes the fact that, in the representation of the overall image defect as a linear combination of the base functions of an orthogonal function set, the overall image defect of the movable and of the stationary optical elements both before as well as after the movement of the movable optical element consists, in a well defined manner, of the individual contributions of the image defects of the movable and of the stationary optical elements. Accordingly conclusions can be drawn as regards the separate image defects of the movable and of the stationary optical elements from two measurements of the overall image defect, namely before and after a movement of the movable optical element. The separate image defects determined in this way may then be used to calculate a target position, i.e. a position of the movable optical element relative to the stationary optical element in which the overall image defect of the optical elements is minimized.
By means of this method the position configuration with the least overall image defect and/or with an overall image defect lying below a specified value is achieved in a deterministic manner, in which no externally determined image quantities but exclusively quantities measured in situ are used. The method can accordingly be automated. Since the method is in principle satisfactorily performed with two measurement steps, it can be carried out relatively quickly and could in principle also be used to take account of varying image properties of the optical elements. In this case the method would be repeated from time to time.
A further object of the invention is to provide methods for optimizing the image properties of at least three optical elements, in which the relative position of the optical elements with respect to one another is adjusted, and by means of which the overall image defect of the optical elements can be specifically minimized with comparatively little effort.
This object is achieved according to the invention by a first method involving the following procedural steps:
a) measurement of the overall image defect of all optical elements, consisting of the image defect of the movable elements and the image defect of the stationary optical element, in which all optical elements are traversed by measuring light;
b) representation of the measured overall image defect as a linear combination of the base functions of an orthogonal function set;
c) movement of one or more of the movable optical elements jointly to a new measurement position;
d) renewed measurement of the overall image defect of the optical elements, consisting of the image defect of the one moved element or of the jointly moved optical elements, and the image defect of the remaining optical elements, in which all optical elements are traversed by measuring light;
e) representation of the new overall image defect as a linear combination of the base functions of an orthogonal function set;
f) calculation of the image defects of the one moved optical element or of the jointly moved optical elements and of the image defect of the remaining optical elements, using the representations obtained in steps b) and e);
g) repetition of the procedural steps c) to f) for one other or several others of the optical elements, until each movable optical element has been moved at least once relative to the closest adjacent optical element or elements;
h) calculation of a target position of the movable optical elements from the image defects of the individual movable optical elements and the at least one stationary optical element, in which the overall image defect is minimized;
i) movement of the movable optical elements to the calculated target position.
With this method the basic principle of the first method according to the invention is developed further in that first of all the separate image defects of all optical elements movable with respect to one another are determined. Then on the basis of the calculated separate image defects of the optical elements that are movable with respect to one another, a target position of the movable optical elements is determined, in which the overall image defect is minimized. Since on account of the representation of the image defects as a linear combination of the base functions of an orthogonal function set the change of the overall image defect as a consequence of the movement of the movable optical elements can be calculated, it is not necessary actually to achieve all possible relative positions of the movable elements in order to optimize the projection objective lens system. Instead, it is sufficient to move each movable optical element at least once relative to the optical elements adjacent thereto. This significantly reduces the number of required movement steps and thus the effort involved in determining a position configuration with optimized image properties. After the determination of the individual image defects, the determination of the target position is a deterministic computational task, which means that only the target position needs to be adjusted.
When calculating the target position either all position combinations of the optical elements movable with respect to one another can be investigated in an imaginary manner, i.e. not by real relative movement but by calculation, and in this way the global minimum of the overall image defect can be determined. Alternatively a statistical procedure can be adopted, in which randomly determined position combinations are tested, and in this way an approximation to the global minimum becomes possible without having to calculate each possible position combination. A statistical procedure that may be used for this purpose can be obtained by transferring a problem from statistical mechanics, namely the determination of the state of a physical multiparticle system in thermal equilibrium. This considerably reduces the computational effort involved in the calculation of the target position.
The last mentioned task is achieved according to the invention by a second method involving the following procedural steps:
a) subdivision of the at least three optical elements into a first part to be moved, and a second, stationary part;
b) measurement of the overall image defect of all optical elements in an initial position, in which all optical elements are traversed by measuring light;
c) representation of the measured image defect as a linear combination of the base functions of an orthogonal function set;
d) movement of the part of the optical elements to be moved, to a new measurement position;
e) renewed measurement of the new overall image defect of all optical elements in the new measurement position, in which the optical elements are traversed by measuring light;
f) representation of the new overall image defect as a linear combination of the base functions of an orthogonal function set;
g) calculation of the image defect of the moved part of the optical elements and of the image defect of the stationary part of the optical elements, using the representation obtained in steps c) and f);
h) calculation of a target position of the moved part or of the previously moved parts of the optical elements, in which the overall image defect is minimised, from the calculated image defects of the moved part and of the stationary part of the optical elements;
i) comparison of the determined overall image defect in the calculated target position with a preset value;
j) if the overall image defect is greater than the preset value and there still exists at least one part of the optical elements already measured with regard to the image defect after the steps a) to g), together with at least two optical elements movable with respect to one another:
ja) determination of that part of the optical elements already measured with regard to the image defect after the steps a) to g) that still consists of at least two optical elements movable relative to one another and exhibits the largest image defect;
jb) subdivision of the determined part of the optical elements into a next part of the optical elements to be moved and into a next stationary part;
jc) repetition of the procedural steps d) to i) for the next part to be moved;
jd) if no subdivisible part according to step jb) exists any longer, the overall image defect is issued and the adjustment procedure is terminated;
k) if the overall image defect is less than the preset value, the moved part or the previously moved parts are moved to the target position calculated in step h) unless this has already occurred within the scope of step i).
With this method it is ensured that a subdivision into movable and stationary parts of the optical elements is carried out only until a predetermined specification of the overall image defect is achieved. In practice initially those parts may be predetermined as movable that according to experience provide the largest image defect contribution. Only if a correction of the overall image defect does not produce the desired effect through the movement of these parts are new subdivisions automatically carried out. This considerably reduces the effort involved in determining the optimized position configuration.
In order to calculate the target position, alternatively all position combinations of the previously moved parts may be reinvestigated and the global minimum may be sought, or instead a statistical procedure as mentioned above may be adopted.
The determination of the new overall image defect before the comparison with the preset value in procedural step i) may comprise the following steps:
a) movement of the moved part of the optical elements to the calculated target position;
b) measurement of the new overall image defect of all optical elements in the target position.
With this modification the calculated target position is monitored as regards the overall image defect by an actual, and thus not only an imaginary, movement of the optical elements to the target position. If there are variations between the calculated and the measured overall image defect in the target position, then a determination of the image defects of the individual previously moved optical elements may optionally be carried out once more.
Alternatively, the overall image defect may be determined before the comparison with the preset value in procedural step i):
Calculation of the new overall image defect of all optical elements in the target position from the calculated image defects of the moved and of the stationary part of the optical elements.
In this case the movement to target positions is omitted so long as it is still not clear whether the overall image defect lies within the specified value. This speeds up the method.
The at least one moveable optical element may be rotatable about the optical axis. By rotating optical elements, non-rotationally symmetrical image defects of optical elements movable with respect to one another can be mutually compensated. In principle the methods according to the invention can also be used to correct image properties by means of other degrees of freedom of movement of the moveable optical elements.
Air image data may be used for the measurement of the overall image defect. Such data based on an intensity measurement in the region of the image plane of the optical element or a plane conjugate thereto may be obtained relatively easily.
An accurate description of the overall image defect is then possible if, for the measurement of the overall image defect, the wave front data of an image bundle are measured after the projection objective lens system. Such an accurate description of the overall image defect ensures a unique allocation of individual defect contributions, which in many cases is a precondition for minimizing the overall image defect within the framework of the optimization method.
The air image data may be measured at various illumination settings. Air image measurements can be carried out with relatively little effort, but as a rule provide unequivocal information only with regard to the azimuthal variation of the overall image defect. If an overall image defect obtained by an air image measurement is matched by means of a linear combination of orthogonal functions, then the problem arises that the radial variations of the overall image defect cannot be matched unequivocally since the accuracy of the air image measurements is as a rule not sufficient for this purpose. If air image data are collected at different illumination settings, then wave front data that are sufficiently accurate for the allocation of individual error contributions can also be obtained via air image measurements. The implementation of more complicated measurement methods, in particular interferometry measurements, in order to determine the wave front data can thus be dispensed with.
Zernike functions may be chosen as orthogonal function set. Zernike functions are routinely used to describe typical image defects, for example Seidel aberrations. The Zernike coefficients may often be allocated directly to a specific image defect, which is why a factorization according to Zernike functions provides a directly readable prediction as regards the image properties of optical elements. The methods according to the invention can of course also be carried out by factorization into other orthogonal function sets, for example Legendre polynomials.